The representation of multispecies chemical transformations into models for porous media flow and transport is investigated. Since the rate of transformation is dependent on the actual concentrations of the reactants inside the pore-spaces (rather than the averaged concentration that is amenable to a porous continuum model) such models may show a lesser or greater rate of transformation than is actually occurring, depending on the pore-scale correlation of the reactant concentrations. To examine this experimentally, a bimolecular reaction (A + B → Product) in a saturated porous media flow in a column was studied using a spectrophotometer. The second-order rate constant of the reaction was independently determined in well-mixed batch tests. In the reactive transport experiments, the porous medium column was initially saturated with one reactant, the other reactant was injected at one longitudinal end of the column, and the effluent concentrations were measured. It is documented that a reactive transport model that does not account for the pore-scale segregation of reactants can substantially overpredict the product concentration.
The concentration variance, i.e., mean squared concentration fluctuations, undergoes mean advection, a local dispersive flux, and a macrodispersive flux due to a correlation between squared concentration perturbations and velocity perturbations. The products of the macrodispersion coefficient and the squared gradient of the mean concentration field determine the rate of production of concentration variance. The rate of dissipation of concentration variance is determined by the product of the local dispersion coefficient and the mean squared gradient of the concentration perturbation field. Variance dissipation is represented as a first-order decay with the decay coefficient equal to twice the sum of the local dispersion coefficient divided by the squared concentration microscale. The concentration microscale, estimated for an advection-dominated log hydraulic conductivity microscale, is an increasing function of the log conductivity microscale. Thus the larger the log conductivity microscale is, the slower is the rate of dissipation of concentration fluctuations by local dispersion and vice versa. The wave number squared dependence of fluctuation dissipation requires intensive sampling to realistically model the log conductivity spectrum and its microscale, which determines the rate of dissipation of concentration fluctuations by the action of local dispersion. There is no mechanism of destroying concentration fluctuations without the action of local dispersion. 1. Introduction The spatially varying velocity field resulting when a saturated porous medium with a spatially varying hydraulic conductivity is subjected to a hydraulic head difference creates rates of growth of the spatial second moments of plumes that are greater than what would occur by local dispersion alone in the uniform mean velocity field. Theoretical studies [e.g., GeIhar and Axness, 1983; Dagan, 1984; Winter eta!., 1984; Gelhar, 1987] have explicitly related this enhanced rate of growth of spatial second moments to the characteristics of the velocity field and thus to the hydraulic conductivity field properties. An effective advection dispersion equation containing an effective dispersion coefficient is used to model the ensemble averaged concentration field. The rate of growth of the spatial second moments of the ensemble averaged concentration field is determined by the effective dispersion coefficient. This requires that there be a scale disparity between the smoothly varying mean concentration field and the rapidly varying hydraulic conductivity. Depending on the heterogeneity encountered, the spatial second moment will show fluctuations around the growing mean [Smith and Schwartz, 1980; Frind et al., 1987; Tompson and Ge!har, 1990]. Rajaram [1991] has shown that the fluctuations in the spatial second moment, as a fraction of its mean value, die out in time. The ensemble averaged equation applies under conditions of sufficient smoothness of the mean concentration field, insofar as it predicts the field-scale spatial second moments of plumes...
Abstract. The concentration of solute undergoing advection and local dispersion in a random hydraulic conductivity field is analyzed to quantify its variability and dilution.
After an initial increase in the absolute value of the segregation intensity, it slowly decreases with time due to the cumulative smoothing action of diffusion. As in hydrologic problems, the diffusion timescales characteristic to the flow variability scales can be quite large; substituting mean concentrations into rate expressions determined in well-mixed batch tests is likely to overestimate the chemical transformation rate. MotivationConcentrations of contaminants undergoing transport and reactions in naturally heterogeneous environments need to be assessed to deal with pollution problems. Consider the inadvertent introduction of wastewater into groundwater. If the organic content of the wastewater is large, the dissolved oxygen in the groundwater can be rapidly depleted. The transport of oxygen from surrounding regions will then control the natural degradation. This transport of oxygen may occur due to advection or small-scale mixing mechanisms (diffusion or local dispersion). As the contaminants get channeled into the high hydraulic conductivity zones, oxygen will get rapidly depleted
For a multidimensional finite-size impulse input, analytical solutions to the conservation equation for concentration variance Crc 2 are presented. Due to the dissipating action of local dispersion, at large times, cr c is a decreasing fraction of the mean concentration. The Cape Cod bromide tracer exhibits this decrease. The larger the log conductivity microscale is, the slower is the action of local dispersion, and the slower is the predicted rate of decrease of the ratio of cr c and the mean concentration (i.e., the coefficient of variation) with time, at large times, and vice versa. The coefficient of variation increases with distance from the center. A balance between the 2 relates it linearly to the squared gradients of rates of production and dissipation of cr c the mean concentration field, away from the center of mass. For the zero local dispersion case, rr c is an unboundedly growing multiple with time of the mean concentration. The longitudinal spatial second moment and macrodispersivities are insensitive to the inclusion/exclusion of local dispersion and therefore do not differentiate between the concentration fields for the two different cases. In contrast, 2 is singularly determined by the dissipating action the spatial-temporal evolution of rr c of local dispersion. Measurements of local dispersivities need to be made along with a characterization of hydraulic conductivity variations to assess contarninant concentrations in aquifers. KAPOOR AND GELHAR: THREE-DIMENSIONALLY HETEROGENEOUS AQUIFERS, 2
This paper describes the Elliptic Curve Cryptography algorithm and its suitability for smart cards. 1 Information Security Information security is essential for today's world since, for profitable and legal trading, confidentiality, integrity and non-repudiability of the associated information are necessary. This can be done using cryptographic systems. Intgerated cryptographic systems satisfy all the above-mentioned requirements. Desired properties of a secure communication system may include any or all of the following[wik, PVO96]: Confidentiality Only an authorized recipient should be able to extract the contents of the encoded data, in part or whole. Integrity The recipient should be able to establish if the message has been altered during transmission. Authentication The recipient should be able to identify the sender, and verify that the purported sender actually sent the message. Non-Repudiation The sender should not be able to deny sending the message, if he actually did send it. Anti-replay The message should not be allowed to be sent to multimple recipients, without the sender's knowledge. Proof of Delivery The sender should be able to prove that the recipient received the message.
Abstract. A three-dimensional analytical model is developed to quantify the process of oxygen-limited biodegradation as it occurs at field scales. The model incorporates the effects of chemical and microbiological heterogeneities inherent to the biodegradation process in a stochastic analysis of the coupled transport equations for a system consisting of a contaminant and an oxidizing agent, that is, oxygen, in heterogeneous and anisotropic aquifers. Natural aquifer variability, equilibrium linear sorption and Monod-type kinetics for the microbial population constitute the sources of these heterogeneities. Calculations for hypothesized field conditions show that longitudinal macrodispersivities for the contaminant and dissolved oxygen are considerably affected by biodegradation. The effective contaminant decay rate is fundamentally found to be moderately less than the mean, while the effects are lesser for the effective retardation factor. The usual assumption of equal dispersivities for both components is found to be inadequate over most concentration ranges.
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